Theory of Ice Sheet Dynamics

This seminar will cover the fundamentals of the theory of ice-sheet dynamics. While the focus will be on viscous ice-sheet flow, we will cover heat flow, basal sliding, hydrology more briefly later in the semester.

We will start from first-principles and introduce all the key concepts needed to build an ice flow model, including stress, strain, rheology, vector calculus, tensors, stress balance, mass conservation. We will use these concepts to derive the simplest possible ice flow models (e.g., assuming perfectly plastic rheology, the shallow ice approximation) and build in complexity from there. We will use these models to build intuition for the first-order dynamics of ice sheets, by examining them analytically and numerically where appropriate. We will use a similar approach for the other topics later in the semester.

As well as a better understanding of ice-sheet dynamics, our aim will be to introduce students to mathematical modelling, demonstrating the overall approach, key concepts will nondimensionalization, and the power of simple models for understanding how natural systems work. We will also aim to build proper intuition for what partial differential equations and solutions to them really are.

Many of these topics could be useful in areas outside glaciology and anyone interested is encouraged to join us.